2 * Copyright 1998-2021 The OpenSSL Project Authors. All Rights Reserved.
4 * Licensed under the Apache License 2.0 (the "License"). You may not use
5 * this file except in compliance with the License. You can obtain a copy
6 * in the file LICENSE in the source distribution or at
7 * https://www.openssl.org/source/license.html
10 #include "internal/cryptlib.h"
13 int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)
16 * like BN_mod, but returns non-negative remainder (i.e., 0 <= r < |d|
20 if (!(BN_mod(r, m, d, ctx)))
24 /* now -|d| < r < 0, so we have to set r := r + |d| */
25 return (d->neg ? BN_sub : BN_add) (r, r, d);
28 int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
33 return BN_nnmod(r, r, m, ctx);
37 * BN_mod_add variant that may be used if both a and b are non-negative and
38 * less than m. The original algorithm was
40 * if (!BN_uadd(r, a, b))
42 * if (BN_ucmp(r, m) >= 0)
43 * return BN_usub(r, r, m);
45 * which is replaced with addition, subtracting modulus, and conditional
46 * move depending on whether or not subtraction borrowed.
48 int bn_mod_add_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
51 size_t i, ai, bi, mtop = m->top;
52 BN_ULONG storage[1024 / BN_BITS2];
53 BN_ULONG carry, temp, mask, *rp, *tp = storage;
54 const BN_ULONG *ap, *bp;
56 if (bn_wexpand(r, mtop) == NULL)
59 if (mtop > sizeof(storage) / sizeof(storage[0])) {
60 tp = OPENSSL_malloc(mtop * sizeof(BN_ULONG));
65 ap = a->d != NULL ? a->d : tp;
66 bp = b->d != NULL ? b->d : tp;
68 for (i = 0, ai = 0, bi = 0, carry = 0; i < mtop;) {
69 mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
70 temp = ((ap[ai] & mask) + carry) & BN_MASK2;
71 carry = (temp < carry);
73 mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
74 tp[i] = ((bp[bi] & mask) + temp) & BN_MASK2;
75 carry += (tp[i] < temp);
78 ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
79 bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
82 carry -= bn_sub_words(rp, tp, m->d, mtop);
83 for (i = 0; i < mtop; i++) {
84 rp[i] = (carry & tp[i]) | (~carry & rp[i]);
85 ((volatile BN_ULONG *)tp)[i] = 0;
88 r->flags |= BN_FLG_FIXED_TOP;
97 int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
100 int ret = bn_mod_add_fixed_top(r, a, b, m);
108 int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
111 if (!BN_sub(r, a, b))
113 return BN_nnmod(r, r, m, ctx);
117 * BN_mod_sub variant that may be used if both a and b are non-negative,
118 * a is less than m, while b is of same bit width as m. It's implemented
119 * as subtraction followed by two conditional additions.
126 * -2*m < r = a - b < m
128 * Thus it takes up to two conditional additions to make |r| positive.
130 int bn_mod_sub_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
133 size_t i, ai, bi, mtop = m->top;
134 BN_ULONG borrow, carry, ta, tb, mask, *rp;
135 const BN_ULONG *ap, *bp;
137 if (bn_wexpand(r, mtop) == NULL)
141 ap = a->d != NULL ? a->d : rp;
142 bp = b->d != NULL ? b->d : rp;
144 for (i = 0, ai = 0, bi = 0, borrow = 0; i < mtop;) {
145 mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
148 mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
150 rp[i] = ta - tb - borrow;
155 ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
156 bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
159 for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
160 ta = ((ap[i] & mask) + carry) & BN_MASK2;
161 carry = (ta < carry);
162 rp[i] = (rp[i] + ta) & BN_MASK2;
163 carry += (rp[i] < ta);
166 for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
167 ta = ((ap[i] & mask) + carry) & BN_MASK2;
168 carry = (ta < carry);
169 rp[i] = (rp[i] + ta) & BN_MASK2;
170 carry += (rp[i] < ta);
174 r->flags |= BN_FLG_FIXED_TOP;
181 * BN_mod_sub variant that may be used if both a and b are non-negative and
184 int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
187 if (!BN_sub(r, a, b))
190 return BN_add(r, r, m);
195 int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
206 if ((t = BN_CTX_get(ctx)) == NULL)
209 if (!BN_sqr(t, a, ctx))
212 if (!BN_mul(t, a, b, ctx))
215 if (!BN_nnmod(r, t, m, ctx))
224 int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx)
226 if (!BN_sqr(r, a, ctx))
228 /* r->neg == 0, thus we don't need BN_nnmod */
229 return BN_mod(r, r, m, ctx);
232 int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx)
234 if (!BN_lshift1(r, a))
237 return BN_nnmod(r, r, m, ctx);
241 * BN_mod_lshift1 variant that may be used if a is non-negative and less than
244 int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m)
246 if (!BN_lshift1(r, a))
249 if (BN_cmp(r, m) >= 0)
250 return BN_sub(r, r, m);
254 int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
257 BIGNUM *abs_m = NULL;
260 if (!BN_nnmod(r, a, m, ctx))
270 ret = BN_mod_lshift_quick(r, r, n, (abs_m ? abs_m : m));
278 * BN_mod_lshift variant that may be used if a is non-negative and less than
281 int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m)
284 if (BN_copy(r, a) == NULL)
292 max_shift = BN_num_bits(m) - BN_num_bits(r);
296 ERR_raise(ERR_LIB_BN, BN_R_INPUT_NOT_REDUCED);
304 if (!BN_lshift(r, r, max_shift))
308 if (!BN_lshift1(r, r))
313 /* BN_num_bits(r) <= BN_num_bits(m) */
315 if (BN_cmp(r, m) >= 0) {
316 if (!BN_sub(r, r, m))